Design of Experiment Application for Unit Process Development in Semiconductor Manufacturing

Transcription

1 Design of Experiment Application for Unit Process Development in Semiconductor Manufacturing Pavel Nesladek Advanced Mask Technology Center, Rähnitzer Allee 9, Dresden, Germany 4 rd European DoE user meeting, Vienna, June 27 th -28 th

2 Outline Introduction Critical Dimension Uniformity (CDU) optimization at dry etch process Iso-dense bias pattern generator Particle Removal Efficiency mask cleaning Summary 2

3 Introduction Current high end Photomask is manufactured of 6x6x0.25 substrate covered by absorber or phase shift layer. Measurement sites Border Critical dimension (CD) Chip area 3

4 Introduction CD is measured at predefined sites CD variation is evaluated and most frequently expressed as 3s y CDU bubble plot CDU 3s= 5.8 ; range= 9.1 ; CDmean= nm x Y Surface / topo plot interpolated

5 Introduction CD is measured at predefined sites CD variation is evaluated and most frequently expressed as 3s CD histogram CD kernel density Frequency Density s mean 3s CD [nm] CD [nm] 5

6 CDU optimization - design 3 factors fullfactorial design Factors A B 1-9 C 1-9 Response CDU 11 Runs 6

7 CDU optimization - ANOVA DESIGN-EXPERT Plot CDU3 Half Normal plot A: A B: B C: C Half Normal % probability A C B AC 20 0 ANOVA result Effect Analysis of variance table [Partial sum of squares] Sum of Mean F Source Squares DF Square Value Prob > F Model significant A 2.053E E B C 4.855E E AC Curvature < significant Residual 7.488E E-003 Lack of Fit 5.635E E

8 CDU optimization - model Model significant but not correct due to strong curvature. DESIGN-EXPERT Plot CDU 3s X = A: A Y = C: C Design Points C C Actual Factor B: B = 5.00 CDU 3s Interaction Graph C: C DESIGN-EXPERT Plot CDU 3s X = A: A Y = C: C Actual Factor B: B = CDU 3s C: C A: A A: A Solutions A Extend design to central composite B look for other / modified response 8

9 CDU optimization curvature solution 1 Solution 1 - Extend design to central composite 3 factors Central composite design Factors A B 1-9 C 1-9 Response CDU C 2 Blocks Block 1 Runs Block 2 Runs Center points A B 9

10 CDU optimization curvature solution 1 Solution 1 - Extend design to central composite 3 factors Central composite design Factors A B 1-9 C 1-9 Response CDU 2 Blocks Block 1-11 Runs Block 2-8 Runs 10

11 CDU optimization curvature solution 1 ANOVA result Analysis of variance table [Partial sum of squares] Sum of Mean F Source Squares DF Square Value Prob > F Block Model < significant A C C < Residual Lack of Fit E not significant Pure Error Cor Total

12 CDU optimization curvature solution 1 Central composite model describes more appropriate experimental data. Design extended by second block DESIGN-EXPERT Plot CDU 3s Design Points 9.00 CDU 3s DESIGN-EXPERT Plot CDU 3s One Factor Plot X = C: C Y = A: A Actual Factor B: B = 5.00 A: A X = C: C Design Points Actual Factors A: A = 5.00 B: B = 5.00 CDU 3s C: C C: C 12

13 CDU optimization curvature solution 2 Solution 2 - look for other / modified response Convex CDU footprint - Concave CDU footprint + CDU with sign

14 CDU optimization curvature solution 2 Solution 2 look for other / modified response Modified CDU response 3FF DoE ANOVA result Analysis of variance table [Partial sum of squares] Sum of Mean F Source Squares DF Square Value Prob > F Model < significant C < Curvature < significant Residual Lack of Fit not significant Pure Error Cor Total

15 CDU optimization curvature solution 2 Solution 2 look for other / modified response Concave CDU positive Convex CDU negative Concave CDU negative Convex CDU positive DESIGN-EXPERT Plot One Factor Plot DESIGN-EXPERT Plot One Factor Plot CDU 3s CDU 3s X = C: C X = C: C Design Points Design Points Actual Factors A: A = 5.00 B: B = 5.00 CDU 3s Actual Factors A: A = 5.00 B: B = 5.00 CDU 3s C: C Model predicts minimum CDU at C = 4.85 Optimum predicted on interpolation of center points is rather 6 C: C 15

16 CDU optimization What is the CDU footprint of center point? Convex or concave? concave convex split convex + concave CDU [nm] CDU [nm] CDU [nm] Plot C Normal Plot of Residuals Plot Normal Plot of Residuals C P l o t N o r m a l P l o t o f R e s i d u a l s C Normal % Probability Normal % Probability Normal % Probability Studentized Residuals Studentized Residuals S t u d e n t i z e d R e s i d u a l s Solution 3 fit of CDU components radial + linear or PCA components fit as work around. May contribute minor CDU improvement. 16

17 CDU optimization - summary CDU result summary Optimum conditions & CDU prediction Raw data Central composite design Modified CDU response Model / A,C,AC A;C;C 2 C conditions A=90; B=9; C=9 A=9; C=4.85 C = 4.85 Curvature Yes NA Yes p < < CDU [nm] predicted CDU [nm] expected Modified response results in same process as central composite design with less effort and material invested. CDU footprint of center points can be estimated using surface fits leading to several CDU component responses. 17

18 Iso-dense bias - introduction Iso- dense bias CD difference between isolated features (A) and nominally same feature in a dense field (C). A<B<C<D A Iso-dense bias is manifestation of proximity effect similar to through pitch CD A>B>C>D or fogging effect. A B C D Fogging effect can be compensated By combination of 2 pattern generator Settings dose, PEC. iso-dense bias is optimized for both Contrasts clear + dark B C D Proximity effect pattern Through pitch pattern 18

19 Iso-dense bias - introduction Iso-dense bias optimization is performed as matrix or PEC pattern written at different dose-pec combination on one mask. PEC Dose 19

20 Iso-dense bias - design Iso-dense Bias experiment is evaluated as historical data DoE with 80 data points, Factors Dose PEC Responses ID-dark bias ID-clear bias (iso-dense biases for clear and dark features) 8 Dose levels 10 PEC levels 20

21 Iso-dense bias - design Iso-dense Bias placement vs. factor space placement on the mask PEC/dose dose PEC 21

22 Iso-dense bias - ANOVA ANOVA result Iso-dense bias clear features Analysis of variance table [Partial sum of squares] Source Sum of Squares DF Mean Square F Value Prob > F Model < significant A-dose < B-PEC < AB < A^ B^ < A^2B AB^ A^ B^ A^2B^ A^3B A^ A^3B^ A^4B Residual Cor Total Model for ID-dark has significant terms up to A^6, B^4 22

23 Iso-dense bias - diagnostics Normality check fails for runs at extreme conditions. Leverage mirrors the mask designs Normal Plot of Residuals 1.00 Leverage vs. Run 99 Normal % Probability Leverage Internally Studentized Residuals Run Number 23

24 Iso-dense bias - models Model for ID-clear and ID-dark similar. Both will be optimized for target 0±1nm ID-CL ID-DK A: dose A: dose B: PEC B: PEC 24

25 Iso-dense bias - Graphical optimization Models are strongly no linear, especially the iso-dense bias model for dark features is questionable Overlay Plot A: dose ID-DK: -1 ID-DK: 1 ID-CL: -1 ID-CL: B: PEC 25

26 Iso-dense bias simplified run set runs at PEC = 0 removed not expected process window, acquired for comparisson between different resists only A: dose B: PEC 26

27 Iso-dense bias simplified ANOVA ANOVA result Iso-dense bias clear features without PEC=0 Analysis of variance table [Partial sum of squares] Sum of Mean F Source Squares DF Square Value Prob > F Model < significant A-dose < B-PEC < A^ < A^ Residual Cor Total

28 Iso-dense bias simplified models Models for both ID-clear and ID-dark become optically very similar ID-CL ID-DK A: dose A: dose B: PEC B: PEC 28

29 Iso-dense bias simplified optimization Process window does not changes significantly at optimum conditions; model becomes simple and easier to interpret Overlay Plot A: dose ID-CL: -1 ID-CL: 1 ID-DK: -1 ID-DK: B: PEC 29

30 Particle Removal Efficiency Particle Removal Efficiency (PRE) quantifies the cleaning efficiency of a mask cleaning process. PRE is used as measure for comparison of cleaning processes and tools PRE evaluation PRE ( Ncoat N N Fresh mask contaminated mask cleaned mask coat post ) Dedicated contamination Test cleaning 30

31 Particle Removal Efficiency Cleaning tool schematics r d w d d r a d c a w a j max 31

32 Particle Removal Efficiency - design 2 Factor central composite design Factors Mask chuck speed Arm swing speed (expressed as time needed fro arm swing between reversal points) Response PRE 32

33 PRE2 all total arm speed chuck speed 33

34 Particle Removal Efficiency - ANOVA Analysis of variance table [Partial sum of squares] Sum of Mean F Source Squares DF Square Value Prob > F Model significant A B A B AB E A2B AB Residual Lack of Fit not significant Pure Error Cor Total

35 Particle Removal Efficiency Model failures D E S I G N - E X P E R T P lo t P R E 2 a ll t o t a l N o r m a l P lo t o f R e s id u a ls Normality check of residuals points towards overestimated model Outlier T test identifies 8 runs over 3s Normal % Probability S t u d e n t i z e d R e si d u a l s Nevertheless no better model is available today. Reason missing factor? - possibly the cleaning power coverage 35

36 Particle Removal Efficiency Coverage? What is that? Combination of arm speed and chuck speed form pattern on the mask which is covering more or less uniformly the mask Identical arm swing speed and chuck speed of, reversal point delay 0.181s 0.233s 36

37 Summary CDU optimization CDU optimization of radial pattern performed via Central composite design and full factorial design with modified response provides almost same result. Minor improvement paid by ~ 70% raised costs and rougly doubled experiment time. Iso dense bias optimization Restriction of historical data feeded into DoE analysis simplifies the model PRE investigation Some models are wrong, (but still usable till better model is found) 37

38 Acknowledgement AMTC is a joint venture of GLOBALFOUNDRIES and Toppan Photomasks and gratefully acknowledges the financial support by the German Federal Ministry of Education and Research (BMBF) 38